Unveiling the Nottingham Inversion Instability during the thermo-field emission from refractory metal micro-protrusions

Darius Mofakhami,Benjamin Seznec,Philippe Testé,Tiberiu Minea,Philippe Dessante,Romaric Landfried

doi:10.1038/s41598-021-94443-7

Abstract

The electron emission by micro-protrusions has been studied for over a century, but the complete explanation of the unstable behaviors and their origin remains an open issue. These systems often evolve towards vacuum breakdown, which makes experimental studies of instabilities very difficult. Modeling studies are therefore necessary. In our model, refractory metals have shown the most striking results for discontinuities or jumps recorded on the electron emitted current under high applied voltages. Herein, we provide evidence on the mechanisms responsible for the initiation of a thermal instability during the field emission from refractory metal micro-protrusions. A jump in the emission current at steady state is found beyond a threshold electric field, and it is correlated to a similar jump in temperature. These jumps are related to a transient runaway of the resistive heating that occurs after the Nottingham flux inversion. That causes the hottest region to move beneath the apex, and generates an emerging heat reflux towards the emitting surface. Two additional conditions are required to initiate the runaway. The emitter geometry must ensure a large emission area and the thermal conductivity must be high enough at high temperatures so that the heat reflux can significantly compete with the heat diffusion towards the thermostat. The whole phenomenon, that we propose to call the Nottingham Inversion Instability, can explain unexpected thermal failures and breakdowns observed with field emitters.

Highlights

Modern and future ultra-high-voltage vacuum equipment requires ever better electrical insulation
The Nottingham heat flux eventually reverses at the apex, which causes a displacement of the maximum temperature into the emitter volume
Our results unveil the theoretical possibility for a thermal instability to occur during the field emission of a micrometric refractory metal emitter when its apex temperature exceeds the Nottingham inversion temperature

Summary

Introduction

Modern and future ultra-high-voltage vacuum equipment requires ever better electrical insulation. Under exceptionally high applied electric fields (1 07–109 V/m), several well-identified physical phenomena can cause a series of interdependent events often evolving towards a vacuum breakdown Most of these breakdown events are related to the presence on the cathode of micro/nano-protrusions, whose shape and density depend on the surface r oughness[4]. Let us recall the Nottingham effect comes from the energy balance between the mean energy of the emitted electrons ǫout and that of the replacing electrons ǫin , the so-called Nottingham energy WN = ǫin − ǫout It yields a heat flux at the metal/vacuum interface whose magnitude depends on the emitter current density J, according to the formula N = −WN × J/e where e is the elementary charge. The question of thermal stability in the self-heating process of field-emitting protrusion is an issue for both the domain of field electron sources and high-voltage vacuum insulation

Results

Discussion

Conclusion